OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 9 — Oct. 2, 2013

Gerchberg-Saxton algorithm applied to a translational-variant optical setup

Ricardo Amézquita-Orozco and Yobani Mejía-Barbosa  »View Author Affiliations

Optics Express, Vol. 21, Issue 16, pp. 19128-19134 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (803 KB) Open Access

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The standard Gerchberg–Saxton (GS) algorithm is normally used to find the phase (measured on two different parallel planes) of a propagating optical field (usually far-field propagation), given that the irradiance information on those planes is known. This is mostly used to calculate the modulation function of a phase mask so that when illuminated by a plane wave, it produces a known far-field irradiance distribution, or the equivalent, to calculate the phase mask to be used in a Fourier optical system so the desired pattern is obtained on the image plane. There are some extensions of the GS algorithm that can be used when the transformations that describe the optical setup are non-unitary, for example the Yang-Gu algorithm, but these are usually demonstrated using nonunitary translational-invariant optical systems. In this work a practical approach to use the GS algorithm is presented, where raytracing together with the Huygens-Fresnel principle are used to obtain the transformations that describe the optical system, so the calculation can be made when the field is propagated through a translational-variant optical system (TVOS) of arbitrary complexity. Some numerical results are shown for a system where a microscope objective composed by 5 lenses is used.

© 2013 OSA

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(140.3300) Lasers and laser optics : Laser beam shaping

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: April 26, 2013
Revised Manuscript: June 24, 2013
Manuscript Accepted: July 12, 2013
Published: August 5, 2013

Virtual Issues
Vol. 8, Iss. 9 Virtual Journal for Biomedical Optics

Ricardo Amézquita-Orozco and Yobani Mejía-Barbosa, "Gerchberg-Saxton algorithm applied to a translational-variant optical setup," Opt. Express 21, 19128-19134 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik35, 227–246 (1972).
  2. J. S. Liu and M. R. Taghizadeh, “Iterative algorithm for the design of diffractive phase elements for laser beam shaping,” Opt. Lett.27, 1463–1465 (2002). [CrossRef]
  3. Q. Li, H. Gao, Y. Dong, Z. Shen, and Q. Wang, “Investigation of diffractive optical element for shaping a Gaussian beam into a ring-shaped pattern,” Opt. Laser Technol.30, 511–514 (1998). [CrossRef]
  4. C. Bay, N. Hubner, J. Freeman, and T. Wilkinson, “Maskless photolithography via holographic optical projection,” Opt. Lett.35, 2230–2232 (2010). [CrossRef] [PubMed]
  5. D. C. O’Shea, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE Publications, 2003). [CrossRef]
  6. O. Ripoll, K. Ville, and H. P. Herzig, “Review of iterative Fourier-transform algorithms for beam shaping applications,” Opt. Eng.43, 2549–2556 (2004). [CrossRef]
  7. G. Yang, B. Gu, J. Zhuang, and O. K. Ersoy, “Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt.33, 209–218 (1994). [CrossRef] [PubMed]
  8. Z. Zalevsky and D. Mendlovic, “Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett.21, 842–844 (1996). [CrossRef] [PubMed]
  9. J. W. Goodman, Introduction to Fourier Optics (Roberts & Co, 2005).
  10. A. Shoemaker, 40X Microscope objective, US Patent 3893751 (1975).
  11. M. Born, E. Wolf, and A. B. Bhatia, Principles of Optics (Pergamon Press, 1975).
  12. N. Lindlein, “Simulation of micro-optical systems including microlens arrays,” Journal of Optics A: Pure and Applied Optics4, S1–S9 (2002). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited